Income Taxes - Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Deferred tax assets:
Share-based compensation	$ 3.1	$ 3.3
Deferred compensation	4.1	3.6
Intangible assets	9.9	4.8
Bad debt reserve	4.4	1.3
Tax credit carryforwards	0.2	0.5
Foreign tax credit carryforwards	2.4	5.0	$ 5.1
Other compensation	5.8	2.2
Property and equipment	7.3	0.0
Other	1.9	1.1
Total gross deferred tax assets	55.3	34.7
Less valuation allowance	(12.4)	(8.5)
Deferred tax assets	42.9	26.2
Deferred income tax liabilities:
Unrealized gain on securities	2.4	3.2
Prepaid expenses	3.4	2.2
Property and equipment	0.0	2.6
Pension liability	0.2	0.2
Deferred income tax liabilities	6.0	8.2
Deferred income taxes, net	36.9	18.0
Non-US [Member]
Deferred tax assets:
Foreign net operating loss carryforwards	5.4	2.6
United States [Member]
Deferred tax assets:
U.S. State and local net operating loss carryforwards	9.0	9.2
U.S. federal net operating loss carryforwards	$ 1.8	$ 1.1